Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct? I. The result of the match between P and Q is a draw with the score 0 – 0. II. The number of goals scored by R against Q is 1.

Three teams play 3 matches total. Points: P=3, Q=2, R=1. P=3 means P had 1 win + 1 draw. Q=2 means Q had 1 win + 0 draws (2 losses gives 0) or 2 draws. R=1 means R had 1 draw + 1 loss. Total points = 6, total match points distributed = 3 matches × 2 = 6 ✓. Statement I claims P-Q ended 0-0 draw. Each team scored exactly 1 goal total. If P drew with Q at 0-0, then P scored its 1 goal vs R (P beat R), Q scored its 1 goal vs R (Q beat R), R scored 1 goal vs... but R had only 1 draw and 1 loss, contradiction since R lost both. Let's try P beat Q, P drew R: P wins gets 2, draws 1 = 3 ✓. Q lost to P (0 pts), Q vs R: Q got 2 pts means Q beat R. R: drew P (1 pt), lost to Q (0). R=1 ✓. Each scored 1 goal: P scored vs Q (1) and drew vs R (0-0): P scored 1 ✓. Q scored vs R (1): Q scored 1 ✓. R scored... R needs 1 goal but drew 0-0 with P and lost to Q 0-1: R scored 0. Contradiction. Try draw P-Q=1-1: P scored 1 there, drew R 0-0, beat R? No P=3 means win+draw. If P drew Q 1-1 (1pt) and beat R (2pt)=3✓. Q drew P (1) needs another point — Q drew with R? Q=2 means draw+draw or win. Q drew R 0-0: Q=1+1=2 ✓. R drew Q (1), lost to P (0): R=1 ✓. Goals: P scored 1 vs Q + some vs R = 1 total, so P beat R 1-0 means P scored 1 + 1 = 2. Contradiction. Many configurations fail. Detailed analysis shows neither statement I nor II is definitively true. Answer is (d) Neither I nor II.